Respecting evidence: belief functions not imprecise probabilities

The received model of degrees of belief represents them as probabilities. Over the last half century, many philosophers have been convinced that this model fails because it cannot cmake room for the idea that an agent's degrees of belief should respect the available evidence. In its place they have advocated a model that represents degrees of belief using imprecise probabilities (sets of probability functions). This paper presents a model of degrees of belief based on Dempster-Shafer belief functions and then presents arguments for belief functions over imprecise probabilities as a model of evidence-respecting degrees of belief. The arguments cover three kinds of issue: theoretical virtues (simplicity, interpretability and flexibility); motivations; and problem cases (dilation and belief inertia).

Automated summary

This paper presents a model of degrees of belief based on Dempster-Shafer belief functions and argues for belief functions over imprecise probabilities as a model of evidence-respecting degrees of belief. The arguments cover three aspects: theoretical virtues, motivations, and problem cases.